Calculus II

Code	14635
Year	1
Semester	S2
ECTS Credits	6
Workload	TP(60H)
Scientific area	Mathematics
Entry requirements	There is no entry requirement.
Mode of delivery	Presential classes
Work placements	Not applicable
Learning outcomes	With this Curricular Unit it is intended that students acquire basic knowledge of Differential and Integral Calculus of functions of several variables. At the end of this UC the student should be able to: 1) Calculate limits of functions of several variables; 2) Study the continuity of functions of several variables; 3) Derive functions of several variables; 4) Apply the derivatives to the calculation of maximums and minimums; 5) Integrate functions of several variables; 6) Use integral calculus to determine areas and volumes. 7) Formulate and solve problems using the differential and integral calculus of functions with several variables
Syllabus	1 Real Functions of Several Variables 1.1 Introduction 1.1.1 Algebraic notions 1.1.2 Sets in R^2 and R^3 1.2 Topological notions in R^n 1.3 Functions, Scalar and Vector Fields 1.4 Limits 1.5 Continuity 1.6 1st Order Partial Derivatives 1.7 Differentiability 1.8 Tangent Plane. Linearization 1.9 Directional Derivative 1.10 Higher Order Derivatives. Schwarz's theorem 1.11 Derivative of the Composite Function. Implicit Function 1.12 Free and Conditioned Extremes 2 Integral Calculus in R^n 2.1 Double Integral 2.2 Triple Integral 2.3 Change of variable
Main Bibliography	Alberto Simões, Apontamentos de Cálculo II, UBI. Stewart, James, "Cálculo", Volume II, 5ª edição Thomson Learning, 2001. Lang, S., "Calculus of Several Variables", Undergraduate Texts in Mathematics, Third Edition, Springer-Verlag,1987. Apostol,T.M., "Calculus",Volume II, John Wiley & Sons, 1968. J. Marsden e A. Tromba, Vector Calculus, W H Freeman & Co., 2003. Jaime Carvalho e Silva, Princípios de Análise Matemática Aplicada, Mc Graw Hill, 1999. Cálculo diferencial e integral, vol. I e vol. II, N. Piskounov, Lopes da Silva, 1987. Robert A. Adams, Calculus: A Complete Course, Addison-Wesley, 2006. H. Anton, I. Bivens e S. Davis, Calculus, (Eight Edition), John Wiley & Sons, 2006.
Teaching Methodologies and Assessment Criteria	The classes will be theoretical-practical. The professor presents the concepts and results, illustrating the theory with examples and applications. The student is encouraged to participate in classes by solving exercises. Autonomous work is encouraged, consisting mainly of exercises.
Language	Portuguese. Tutorial support is available in English.